Finite Group DatabasebetaFinite Group Databasebeta| order | 34242 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C2×C13×C439⋊C3 |
| unambiguous semidirect product | (C2×C439)⋊(C3×C13) |
| Fitting, socle, Hall | C2×C13×C439 ⋊ C3 |
| derived, Sylow | C439 ⋊ C2×C3×C13 |
| Hall | C13×C439 ⋊ C2×C3 |
| Hall | C2×C439 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | C439⋊C3 |
| commutator, cosocle, hypocenter | C439 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C439 | C3 |
| LCS | G ▷ C439 | |
| UCS | C1 ◁ C2×C13 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11414 |
3874 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34242, 2);